The present invention relates generally to the field of processing and displaying seismic data. More particularly, the present invention is directed to a novel method for identifying and separating the effects of elastic and anelastic formation properties in seismic reflection data.
Broadly, seismic exploration comprises imparting seismic wave energy into the earth's subterranean formations and detecting the earth's response thereto with a plurality of geophones. Geophones produce an electrical signal containing information on the earth's subterranean formations. Such electrical signals can be processed and displayed as seismic sections having a plurality of traces or seismic signals thereon representative of the processed electrical signals from which geophysicists can make interpretations of the earth's subterranean formations.
As seismic wave propagates through the earth's subterranean formations, its energy is dissipated as a function of distance traveled due to wave front spreading, absorption, and partitioning of the seismic energy at reflecting boundaries.
In terms of a propagating sinusoidal signal, such as a seismic signal, the decrease in seismic energy due to absorption over a distance L can be described according to: EQU A=A.sub.o e.sup.-.alpha.L ( 1)
where A.sub.o is the initial signal amplitude, and .alpha. is the absorption coefficient over the distance traveled.
The absorption coefficient .alpha. is defined in terms of the decrease of signal amplitude per unit distance. Other measurements of absorptive loss per cycle can be characterized by the following: EQU A=A.sub.o e.sup.-.delta. ( 2)
where .delta.=(logarithmic decrement)=.alpha..lambda. PA1 where .lambda.=wavelength=V/f (V=velocity, f=frequency) PA1 V.sub.i is the seismic velocity of the ith formation, and PA1 A.sub.R /A.sub.i is the ratio of the reflected to incident signal amplitude.
Partitioning of the seismic wave energy at reflecting boundaries depends on the elastic properties (e.g., density and seismic wave velocities) and the anelastic properties ( e.g., absorptive loss) of the formation on either side of the reflecting boundary and the angle of incidence and frequency content of the seismic wave. In perfectly elastic formations, partitioning depends only on the elastic properties of the formations on either side of a reflecting boundary, and also on the angle of incidence of the seismic wave with respect to the reflecting boundary.
For perfectly elastic media, the relationship which governs partitioning at a reflecting boundary is given by the following (for normal incidence): ##EQU1## where .delta..sub.i is the density of the ith formation,
As used herein, a contrast in either elastic or anelastic properties across a reflecting boundary in the earth's subterranean formations is understood to comprehend a difference in the elastic or anelastic properties of the earth's subterranean formations on either side of the reflecting boundary. Similarly, an impedance or absorptive contrast across a reflecting boundary in the earth's subterranean formations is understood to comprehend a difference in the impedance or absorptive properties of the earth's subterranean formations on either side of the reflecting boundary.
Present seismic signal analysis techniques are predicated upon the assumption that only elastic contrasts affect the partitioning of seismic wave energy (amplitude and phase of the reflected and transmitted seismic energy) for subcritical incidence, i.e., it assumes perfectly elastic subterranean formations. In such case, changes in the phase of the seismic signal at simple reflecting boundaries can only be either 0.degree. or 180.degree.. However, for a compound reflection, i.e., from a thin subterranean bed, e.g., generally less than 1/4 wavelength in thickness may also produce intermediate phase changes. However, when anelastic contrasts are considered, as disclosed herein, the change in phase can take on a range of values between 0.degree. and 360.degree.. As such, the present techniques for processing seismic signals from subterranean formations in which significant anelastic contrasts exist across a reflecting boundary are simply in error.
The present invention discloses a technique whereby the effects of impedance and absorptive contrasts within the earth's subterranean formations on a seismic signal can be separately decomposed. The resultant decompositions can be more properly analyzed in terms of the elastic and anelastic properties of the earth's subterranean formations. Additionally, comparison of the resultant decompositions of the seismic signal into its elastic component and anelastic component can provide a measure of the error in a seismic signal which assumes only elastic contrasts across reflecting boundaries; or equivalently, a measure of the earth's subterranean formations absorptive properties. The present invention also discloses a method for distinguishing a gas containing formation from a similar formation containing a liquid.